Model-independent Constraints on the Weak Phase $α$ (or $ϕ_2$) and QCD Penguin Pollution in $B \to ππ$ Decays

Abstract

We present an {\it algebraic} isospin approach towards a more straightforward and model-independent determination of the weak phase $α$ (or $ϕ_2$) and QCD penguin pollution in $B\to ππ$ decays. The world averages of current experimental data allow us to impose some useful constraints on the isospin parameters of $B\to ππ$ transitions. We find that the magnitude of $α$ (or $ϕ_2$) extracted from the indirect CP violation in $π^+π^-$ mode is in agreement with the standard-model expectation from other indirect measurements, but its four-fold discrete ambiguity has to be resolved in the near future.